@article{Agarwal2012OnRS,
title={On Range Searching with Semialgebraic Sets II},
author={P. Agarwal and J. Matousek and M. Sharir},
journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
year={2012},
pages={420-429}
}

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

Let P be a set of n points in Rd. We present a linear-size data structure for answering range queries on P with constant-complexity semialgebraic sets as ranges, in time close to O(n1-1/d). It essentially matches the performance of similar structures for simplex range searching, and, for d ≥ 5, significantly improves earlier solutions by the first two authors obtained in 1994. This almost settles a long-standing open problem in range searching. The data structure is based on the polynomial… CONTINUE READING